The making of an exponential Diophantine equation.

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[hydraslair]

I love these "make your own problem" style videos! They give twice as much insight on problems

[abrahammekonnen]

These problem building videos are really interesting because they force us to see math from a different perspective.
As usual this video was pretty great.

[romajimamulo]

10:02 15 is divisible by 3, it's not a power of three though

[pajrc]

You can also eliminate 2*28 by seeing that since one is 3^a-5^b and the other is 3^a+5^b, their difference must be twice a power of 5, which only applies to 4*14

[Roshkin]

I believe you mean power not mulitple at the end for 3^a = 15

[stkhan]

..michael penn ...always a joy to watch your math content.. thnq

[noproof]

Thank you Michael Penn, you are a legend

[kenbrady]

New merchandising idea: shirts with sleeves that can be used as erasers!

[SR-mldn]

Thanks Michael Penn, your videos are always very educational. I didn't know the fact or having thought about adding or subtracting even numbers and they then become odd numbers. Diophantine solving for the right polynomials occurs quite often in solving adaptive controllers for control purpose.

[sunilsheth]

just learnt how problems are generated! very nice presentation.

[mcwulf]

This looks like fun. No need to hunt number theory problems any more - just make my own 😁

[hassanalihusseini]

Thank you for this inspiring video! It is good to see how to build some exercises.

[tonyg]

This channel made me realize just how much math I don't understand. I don't think I've seen a single video in which I could have solved the problem on my own.

[pauliusasvydis]

You can also get that m, n are even by checking mod 4, in general for any exponential diophantine equation checking mod 3, mod 4 usually gives some interesting results.

[mikewise]

Michael Penn, your videos are amazing!

Now's a good place to stop this comment.

[Pfs]

#6:31 why is m=4a+1 and n=4b+3 not a posibility?

[nadermaleklou]

Nice video as always
In some equations, we need to check the remainder on division by sth . How does the person who makes the problem know which polynomials or numbers give us unique answer or contradiction ?

[piotrtrzcinski]

I really hoped for a proof that exponentiation is Diophantine

[juanpablosimonetti]

Me encantó que propusieras este video enseñando a armar problemas. Muchas Gracias!
I loved that you proposed this video teaching how to set up problems. Thank you very much!

[snehasismaiti]

Can anyone solve this for me:- Show that there are infinitely many pairs (a, b) of coprime integers (which may be negative, but not zero) such that x^2 + ax + b = 0 and x^2 + 2ax + b have integral roots.